Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem

This paper presents an integer programming model for developing optimal shift schedules while allowing extensive flexibility in terms of alternate shift starting times, shift lengths, and break placement. The model combines the work of Moondra (1976) and Bechtold and Jacobs (1990) by implicitly matching meal breaks to implicitly represented shifts. Moreover, the new model extends the work of these authors to enable the scheduling of overtime and the scheduling of rest breaks. We compare the new model to Bechtold and Jacobs' model over a diverse set of 588 test problems. The new model generates optimal solutions more rapidly, solves problems with more shift alternatives, and does not generate schedules violating the operative restrictions on break timing.

Labor Scheduling Using NPV Estimates of the Marginal Benefit of Additional Labor Capacity

An extensive literature exists on the problems of daily (shift) and weekly (tour) labor scheduling. In representing requirements for employees in these problems, researchers have used formulations based either on the model of Dantzig (1954) or on the model of Keith (1979). We show that both formulations have weakness in environments where management knows, or can attempt to identify, how different levels of customer service affect profits. These weaknesses results in lower-than-necessary profits. This paper presents a New Formulation of the daily and weekly Labor Scheduling Problems (NFLSP) designed to overcome the limitations of earlier models. NFLSP incorporates information on how changing the number of employees working in each planning period affects profits. NFLP uses this information during the development of the schedule to identify the number of employees who, ideally, should be working in each period. In an extensive simulation of 1,152 service environments, NFLSP outperformed the formulations of Dantzig (1954) and Keith (1979) at a level of significance of 0.001. Assuming year-round operations and an hourly wage, including benefits, of $6.00, NFLSP's schedules were $96,046 (2.2%) and $24,648 (0.6%) more profitable, on average, than schedules developed using the formulations of Danzig (1954) and Keith (1979), respectively. Although the average percentage gain over Keith's model was fairly small, it could be much larger in some real cases with different parameters. In 73 and 100 percent of the cases we simulated NFLSP yielded a higher profit than the models of Keith (1979) and Danzig (1954), respectively.

Multi-stage scheduling problems with precedence constraints

Abstract not available

A heuristic algorithm for the two-machine re-entrant shop scheduling

Abstract not available

Heuristics for the two-stage job shop scheduling problem with a bottleneck machine

Abstract not available

Heuristics for short route job shop scheduling problems

Abstract not available

Two-stage open shop scheduling with a bottleneck machine

Abstract not available

Two-machine open shop scheduling with special transportation times

Abstract not available

Assembly scheduling with batching

Abstract not available

Flow shop scheduling problems under machine-dependent precedence constraints

Abstract not available

A Research of Resource Scheduling Algorithm Based on Hadoop

With the development of electronic devices, more and more mobile clients are connected to the Internet and they generate massive data every day. We live in an age of “Big Data”, and every day we generate hundreds of million magnitude data. By analyzing the data and making prediction, we can carry out better development plan. Unfortunately, traditional computation framework cannot meet the demand, so the Hadoop would be put forward. First the paper introduces the background and development status of Hadoop, compares the MapReduce in Hadoop 1.0 and YARN in Hadoop 2.0, and analyzes the advantages and disadvantages of them. Because the resource management module is the core role of YARN, so next the paper would research about the resource allocation module including the resource management, resource allocation algorithm, resource preemption model and the whole resource scheduling process from applying resource to finishing allocation. Also it would introduce the FIFO Scheduler, Capacity Scheduler, and Fair Scheduler and compare them. The main work has been done in this paper is researching and analyzing the Dominant Resource Fair algorithm of YARN, putting forward a maximum resource utilization algorithm based on Dominant Resource Fair algorithm. The paper also provides a suggestion to improve the unreasonable facts in resource preemption model. Emphasizing “fairness” during resource allocation is the core concept of Dominant Resource Fair algorithm of YARM. Because the cluster is multiple users and multiple resources, so the user’s resource request is multiple too. The DRF algorithm would divide the user’s resources into dominant resource and normal resource. For a user, the dominant resource is the one whose share is highest among all the request resources, others are normal resource. The DRF algorithm requires the dominant resource share of each user being equal. But for these cases where different users’ dominant resource amount differs greatly, emphasizing “fairness” is not suitable and can’t promote the resource utilization of the cluster. By analyzing these cases, this thesis puts forward a new allocation algorithm based on DRF. The new algorithm takes the “fairness” into consideration but not the main principle. Maximizing the resource utilization is the main principle and goal of the new algorithm. According to comparing the result of the DRF and new algorithm based on DRF, we found that the new algorithm has more high resource utilization than DRF. The last part of the thesis is to install the environment of YARN and use the Scheduler Load Simulator (SLS) to simulate the cluster environment.

Efficient algorithms to solve scheduling problems with a variety of optimization criteria

La programmation par contraintes est une technique puissante pour résoudre, entre autres, des problèmes d’ordonnancement de grande envergure. L’ordonnancement vise à allouer dans le temps des tâches à des ressources. Lors de son exécution, une tâche consomme une ressource à un taux constant. Généralement, on cherche à optimiser une fonction objectif telle la durée totale d’un ordonnancement. Résoudre un problème d’ordonnancement signifie trouver quand chaque tâche doit débuter et quelle ressource doit l’exécuter. La plupart des problèmes d’ordonnancement sont NP-Difficiles. Conséquemment, il n’existe aucun algorithme connu capable de les résoudre en temps polynomial. Cependant, il existe des spécialisations aux problèmes d’ordonnancement qui ne sont pas NP-Complet. Ces problèmes peuvent être résolus en temps polynomial en utilisant des algorithmes qui leur sont propres. Notre objectif est d’explorer ces algorithmes d’ordonnancement dans plusieurs contextes variés. Les techniques de filtrage ont beaucoup évolué dans les dernières années en ordonnancement basé sur les contraintes. La proéminence des algorithmes de filtrage repose sur leur habilité à réduire l’arbre de recherche en excluant les valeurs des domaines qui ne participent pas à des solutions au problème. Nous proposons des améliorations et présentons des algorithmes de filtrage plus efficaces pour résoudre des problèmes classiques d’ordonnancement. De plus, nous présentons des adaptations de techniques de filtrage pour le cas où les tâches peuvent être retardées. Nous considérons aussi différentes propriétés de problèmes industriels et résolvons plus efficacement des problèmes où le critère d’optimisation n’est pas nécessairement le moment où la dernière tâche se termine. Par exemple, nous présentons des algorithmes à temps polynomial pour le cas où la quantité de ressources fluctue dans le temps, ou quand le coût d’exécuter une tâche au temps t dépend de t.

DESIGN, FABRICATION, AND PERFORMANCE CHARACTERIZATION OF MULTIFUNCTIONAL STRUCTURES TO HARVEST SOLAR ENERGY FOR FLAPPING WING AERIAL VEHICLES

Flapping Wing Aerial Vehicles (FWAVs) have the capability to combine the benefits of both fixed wing vehicles and rotary vehicles. However, flight time is limited due to limited on-board energy storage capacity. For most Unmanned Aerial Vehicle (UAV) operators, frequent recharging of the batteries is not ideal due to lack of nearby electrical outlets. This imposes serious limitations on FWAV flights. The approach taken to extend the flight time of UAVs was to integrate photovoltaic solar cells onto different structures of the vehicle to harvest and use energy from the sun. Integration of the solar cells can greatly improve the energy capacity of an UAV; however, this integration does effect the performance of the UAV and especially FWAVs. The integration of solar cells affects the ability of the vehicle to produce the aerodynamic forces necessary to maintain flight. This PhD dissertation characterizes the effects of solar cell integration on the performance of a FWAV. Robo Raven, a recently developed FWAV, is used as the platform for this work. An additive manufacturing technique was developed to integrate photovoltaic solar cells into the wing and tail structures of the vehicle. An approach to characterizing the effects of solar cell integration to the wings, tail, and body of the UAV is also described. This approach includes measurement of aerodynamic forces generated by the vehicle and measurements of the wing shape during the flapping cycle using Digital Image Correlation. Various changes to wing, body, and tail design are investigated and changes in performance for each design are measured. The electrical performance from the solar cells is also characterized. A new multifunctional performance model was formulated that describes how integration of solar cells influences the flight performance. Aerodynamic models were developed to describe effects of solar cell integration force production and performance of the FWAV. Thus, performance changes can be predicted depending on changes in design. Sensing capabilities of the solar cells were also discovered and correlated to the deformation of the wing. This demonstrated that the solar cells were capable of: (1) Lightweight and flexible structure to generate aerodynamic forces, (2) Energy harvesting to extend operational time and autonomy, (3) Sensing of an aerodynamic force associated with wing deformation. Finally, different flexible photovoltaic materials with higher efficiencies are investigated, which enable the multifunctional wings to provide enough solar power to keep the FWAV aloft without batteries as long as there is enough sunlight to power the vehicle.

'Explicit Learning: an Effort towards Human Scheduling Algorithms'

Abstract Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of a general scheduling algorithm is still in its infancy. Mimicking the natural evolutionary process of the survival of the fittest, Genetic Algorithms (GAs) have attracted much attention in solving difficult scheduling problems in recent years. Some obstacles exist when using GAs: there is no canonical mechanism to deal with constraints, which are commonly met in most real-world scheduling problems, and small changes to a solution are difficult. To overcome both difficulties, indirect approaches have been presented (in [1] and [2]) for nurse scheduling and driver scheduling, where GAs are used by mapping the solution space, and separate decoding routines then build solutions to the original problem. In our previous indirect GAs, learning is implicit and is restricted to the efficient adjustment of weights for a set of rules that are used to construct schedules. The major limitation of those approaches is that they learn in a non-human way: like most existing construction algorithms, once the best weight combination is found, the rules used in the construction process are fixed at each iteration. However, normally a long sequence of moves is needed to construct a schedule and using fixed rules at each move is thus unreasonable and not coherent with human learning processes. When a human scheduler is working, he normally builds a schedule step by step following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not completed yet, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this research we intend to design more human-like scheduling algorithms, by using ideas derived from Bayesian Optimization Algorithms (BOA) and Learning Classifier Systems (LCS) to implement explicit learning from past solutions. BOA can be applied to learn to identify good partial solutions and to complete them by building a Bayesian network of the joint distribution of solutions [3]. A Bayesian network is a directed acyclic graph with each node corresponding to one variable, and each variable corresponding to individual rule by which a schedule will be constructed step by step. The conditional probabilities are computed according to an initial set of promising solutions. Subsequently, each new instance for each node is generated by using the corresponding conditional probabilities, until values for all nodes have been generated. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the Bayesian network is updated again using the current set of good rule strings. The algorithm thereby tries to explicitly identify and mix promising building blocks. It should be noted that for most scheduling problems the structure of the network model is known and all the variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus learning can amount to 'counting' in the case of multinomial distributions. In the LCS approach, each rule has its strength showing its current usefulness in the system, and this strength is constantly assessed [4]. To implement sophisticated learning based on previous solutions, an improved LCS-based algorithm is designed, which consists of the following three steps. The initialization step is to assign each rule at each stage a constant initial strength. Then rules are selected by using the Roulette Wheel strategy. The next step is to reinforce the strengths of the rules used in the previous solution, keeping the strength of unused rules unchanged. The selection step is to select fitter rules for the next generation. It is envisaged that the LCS part of the algorithm will be used as a hill climber to the BOA algorithm. This is exciting and ambitious research, which might provide the stepping-stone for a new class of scheduling algorithms. Data sets from nurse scheduling and mall problems will be used as test-beds. It is envisaged that once the concept has been proven successful, it will be implemented into general scheduling algorithms. It is also hoped that this research will give some preliminary answers about how to include human-like learning into scheduling algorithms and may therefore be of interest to researchers and practitioners in areas of scheduling and evolutionary computation. References 1. Aickelin, U. and Dowsland, K. (2003) 'Indirect Genetic Algorithm for a Nurse Scheduling Problem', Computer & Operational Research (in print). 2. Li, J. and Kwan, R.S.K. (2003), 'Fuzzy Genetic Algorithm for Driver Scheduling', European Journal of Operational Research 147(2): 334-344. 3. Pelikan, M., Goldberg, D. and Cantu-Paz, E. (1999) 'BOA: The Bayesian Optimization Algorithm', IlliGAL Report No 99003, University of Illinois. 4. Wilson, S. (1994) 'ZCS: A Zeroth-level Classifier System', Evolutionary Computation 2(1), pp 1-18.

'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.